Swaps work BEST if you both have something that the other person wants to build, but that's not going to happen very often. Swaps and Knowledge Point Clubs work just fine for mutually leveling each other's Ancient Wonders. After all, you only need 18 Runes every 5th level, and some of them are going to come from Tournaments and newly acquired sectors.swaps only work once you have the wonder you want to build.
After all, you only need 18 Runes every 5th level, ...
To capture 5th place the MOST KPs you'll ever need to contribute is 1/6th of 250 = 42 KPs.
The statistical model for filling a Rune Wheel depends on how many trials you'll need to fill one of the REMAINING slots.
- 9/9 + 9/8 + 9/7 + 9/6 + 9/5 + 9/4 + 9/3 + 9/2 = 16.24 trials to fill the first 8 Rune Wheel slots, on average
Or, to state the same concept positively, designed to provide some realistic constraints. While people don't conceptualize them as such, most meatspace activities are chaotic. If they're a slam dunk then we turn them over to a machine because they're not interesting.use some form of a weighted formula designed to impede progress.
- 9/9 + 9/8 + 9/7 + 9/6 + 9/5 + 9/4 + 9/3 + 9/2 = 16.24 trials to fill the first 8 Rune Wheel slots, on average
A Rune Shard will only shatter if it tries to land in a randomly selected slot, and that slot has ALREADY been filled.
- In your FIRST state, which is an empty wheel, a Rune Shard will NEVER shatter.
- In your SECOND state, a Rune Shard will shatter 1 time out of 9
- It's more convenient to say that you'll be successful 8 times out of 9
- And you can express the odds as how many trials you'll need to FILL 8/9ths, it's a simple inversion, which is where we get 9/8ths.
- And you can simply add up the number of trials that you'll need at each stage.
- In your THIRD state, a Rune Shard sill shatter 2 times out of 9, so you'll need 9/7 trials.
- In your FOURTH state, a Rune Shard will shatter 3 times out of 9, so you'll need 9/6 trials.
- Etc. for 16 trials
- In your NINTH state, a Rune Shard will shatter 8 times out of 9, so you'll need 9/1 trials
- This is WHY the Broken Rune Shard Bar is so important. It chops the tail off of the distribution, right when your odds are the worst.
- 18 Trials = 18 Rune Shards per wheel, on average. Tally your results, don't trust your memory.
- If you need fewer than 15 or more than 21 Rune Shards to fill a Wheel, I'd be very interested in looking at your data and your methodology.
The statistical model for filling a Rune Wheel depends on how many trials you'll need to fill one of the REMAINING slots.
- 9/9 + 9/8 + 9/7 + 9/6 + 9/5 + 9/4 + 9/3 + 9/2 = 16.24 trials to fill the first 8 Rune Wheel slots, on average
- You'll have 8 broken shards as well
- Trial 17 will get you either a full wheel or 9 broken shards
- Trial 18 will get you either a full wheel of 10 broken shards, so you're done.
On the second point, I can only give a data point, I didn't record the exact outcome of each rune shard placement - but it took me 27 Shards to fill a wheel, starting from empty. I think I know why, though, and it comes back to the unstated assumption in your 18 Shards figure above - you're assuming the Broken Shard bar is empty to start, and it doesn't fill "too soon".
- 18 Trials = 18 Rune Shards per wheel, on average. Tally your results, don't trust your memory.
- If you need fewer than 15 or more than 21 Rune Shards to fill a Wheel, I'd be very interested in looking at your data and your methodology.
I tried that - I was unable to place a rune until I had cleared the full shard bar. It appeared that, once full, the shard bar must be used to forge a rune before you can place any other runes you might have.Or you could avoid using the full bar, until it counts for more.
I think Jixel has a point. While Katwijk's model is correct in theory, in practice we have runes from multiple wonders and the shard bar is rarely empty at the point where you start to fill a new wheel. In fact, I started my most recent wheel with a full shard bar that had to be forged into a rune.
That said, it is possible to extrapolate from Katwijk's model that even with an unlucky sequence and shard bar status, it shouldn't take more than 27 runes at the outside to fill. That said, I think that is only true if you do it all at once though. If you are using runes as you acquire them, across multiple wonders, then that would (I think) mess with the shard bar status and cost you more runes.
Which is to say - if you want to use the fewest runes possible, wait until you have 15+ runes in the bank before you try to fill the wheel. Or only attempt to fill one wheel at a time. But who has the patience for that?